K-factor calculator for sheet metal bending

What the K-factor tells you

In sheet metal bending, the K-factor locates the neutral axis inside the bend. The neutral axis is the layer of the sheet that neither stretches nor compresses as it bends. The K-factor is its distance from the inside surface, divided by the material thickness.

A flat sheet has its neutral axis at half its thickness. As the sheet bends, the neutral axis moves toward the inside of the bend. In The Fabricator, Steve Benson gives the usual range as 0.50 down to 0.33, and says it can go lower. You need the K-factor to work out the bend allowance, the bend deduction and the flat blank of a part.

This page covers the K-factor of sheet metal bending. A flow meter's K-factor, the number of pulses per unit of volume, is a different quantity with the same name.

How to find the K-factor with a test bend

1. Cut a strip from the sheet you use in production, and measure its length before you bend it. That length is the flat blank.
2. Bend the strip to 90° on your press brake, with the punch and die you use for the job.
3. Measure the inside radius with a radius gauge or a pin gauge.
4. Measure each flange from its edge to the apex of the bend. On a 90° bend, that is the outside dimension of the flange.
5. Enter the six numbers above. The calculator works out the bend allowance from your measurements, then the K-factor.

Benson recommends at least three test pieces of the same grade and thickness, bent the same way and with the grain in the same direction. Work out the K-factor for each piece and average them.

The formulas behind the result

The calculator follows the bend functions in Benson's calculation basics and his K-factor series. T is the thickness, R the inside radius and A the bend angle in degrees.

• Outside setback: OSSB = tan(A / 2) x (R + T)
• Bend deduction measured on the test piece: BD = flange 1 + flange 2 - flat blank
• Bend allowance: BA = 2 x OSSB - BD
• K-factor: K = (180 x BA) / (pi x A x T) - R / T

The last line is Benson's formula from part II of the series. The first three come from his flat blank layout, where the blank equals the two dimensions to the apex minus the bend deduction.

Typical K-factor values

The Fabricator prints a generic chart based on Machinery's Handbook. It gives average K-factors by bending method and by the inside radius compared with the thickness. The chart groups the soft and medium columns under aluminum and the hard column under steel. The calculator shows the air bending range for your R/T next to your result.

Other published values fall in the same range. Benson uses an average of 0.4468 for most bending. Cincinnati Incorporated's bend allowance chart for mild steel air bends prints two formulas, BA = 1.57 (R + 0.4T) and BA = 1.57 (R + T/3). Those are K-factors of 0.4 and one third. Its rows for 16 gauge and thinner match the second formula, and its rows for 15 gauge and thicker match the first.

In a 2023 article, Benson also gives a way to estimate K without a test bend. The estimate is 0.273 plus 0.0756 times R/T, and it stops at 0.50. The 0.273 is the smallest K-factor for air forming, (4 - pi) / pi. His example, a 0.093 in radius in 0.062 in material, gives 0.386. The calculator shows this estimate beside your measured value.

Worked example

You bend a 2 mm strip to 90° in a 16 mm vee die, and it forms a 2.5 mm inside radius. Each flange measures 50 mm to the outside, and the strip measured 96.25 mm before bending.

• Outside setback: tan 45° x (2.5 + 2) = 4.5 mm
• Bend deduction: 50 + 50 - 96.25 = 3.75 mm
• Bend allowance: 2 x 4.5 - 3.75 = 5.25 mm
• K-factor: (180 x 5.25) / (pi x 90 x 2) - 2.5 / 2 = 1.671 - 1.25 = 0.421

R/T is 1.25 here, and the chart's air bending range for R between T and 3T is 0.40 to 0.45, so 0.421 sits inside it. In inches, take a 0.060 in strip with a 0.0625 in radius, two 2.000 in flanges and a 3.893 in blank. It gives a bend allowance of 0.138 in and a K-factor of 0.423.

A K-factor is sensitive to small errors in the measurements. In the example, a flat blank measured 0.05 mm longer moves the K-factor from 0.421 to 0.437. Measure carefully and average several pieces.

What changes the K-factor

• Bending method. Benson cites a study in which bottoming raised the K-factor by 15 percent over air bending, with the same material and tooling. Coining moves the neutral axis back toward the inside.
• Radius and thickness. A smaller inside radius for the thickness pushes the neutral axis inward and lowers K. Thicker and harder material lowers it too, with a die opening that suits the thickness.
• Die width. For the same thickness, a narrower die raises the K-factor.
• Grain direction. A bend parallel to the rolling direction moves the neutral axis inward.

A K-factor from your own brake, tooling and material accounts for all four, which is why Benson recommends one when precision matters.

Using your K-factor

CAD software builds sheet metal flat patterns from a K-factor or a Y-factor, so a measured value makes the flat pattern match your press brake. The bend allowance calculator and the bend deduction calculator take it from here. Benson notes that a K-factor never goes above 0.50, and a wide radius that calculates higher should use 0.50.

When a product comes in many sizes, the K-factor sits inside the rules that produce each flat blank and its price. The guide to product configurator software explains how those rules become a configured, priced part.